Path planning strategies are studied using an optimization model. Four main sub-models are discussed that contribute to the computing of minimum energy vehicle path planning. These are: 1) formal methods of minimization of expended energy given a three dimensional terrain to traverse; 2) drag function estimation, which is a modelling process for determination of the effects of local terrain soil characteristics; 3) analysis of the vehicle/soil interaction process, and 4) graph-searching techniques that combine minimum energy paths in conjunction with safety and traversability to determine an optimal route from the path origin to the desired destination. This paper examines these models to create a practical path planning model to be used for planetary exploration and terrestrial off-road transportation in remote areas.